KNeighborsClassifier欧式距离计算

Question

I have a question regarding KNeighborsClassifier

This is the code I have for iris dataset.

iris = datasets.load_iris()
X = iris.data # Independent variables
y = iris.target # response or target or dependent variables

x_train, x_test, y_train,y_test = (train_test_split(X,y, test_size=0.3,
                                                   random_state=42,
                                                   stratify=y))

knn = KNeighborsClassifier(n_neighbors = 5)
knn.fit(x_train, y_train)
prediction = knn.predict(x_test)
print (accuracy_score(y_test, prediction))

So I know the distance between two points are calculated using Euclidean Distance.

For example train iris data set has 4 features and test iris data set also has 4 features so how is euclidean distance calculated between these 4 column values. Assume this is our train data

array([[5.1, 2.5, 3. , 1.1],
       [6.2, 2.2, 4.5, 1.5],
       [5.1, 3.8, 1.5, 0.3],
       [6.8, 3.2, 5.9, 2.3]]

And this is our test data

array([[7.3, 2.9, 6.3, 1.8],
       [6.1, 2.9, 4.7, 1.4],
       [6.3, 2.8, 5.1, 1.5],
       [6.3, 3.3, 4.7, 1.6]]

How is the Euclidean distance calculated for four points?

Answer 1

Same as you would for two points on a plane, or for 3 points in a 3D space - but now extended to a 4 dimensional vector space:

sqrt((a1-b1)^2+(a2-b2)^2+(a3-b3)^2+(a4-b4)^2)

This extends to any number of dimensions